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Sagot :
The magnitude of the change in A that occurs is; A_a/A_w = 1.8
Magnitude of Change in Amplitude
From the complete question online,
The ear tries to conserve the energy in the wave I,
I = 2π²vρυ²Α²
where;
v is the wave speed
ρ is the density of the medium
υ is the frequency of the wave
A is the amplitude of the wave
We are given;
Density of air; ρ_a = 1.3 × 10⁻³ g/cm³ = 1300 kg/m³
Density of water; ρ_w = 1.0 g/cm³ = 1000 kg/m³
Velocity of sound in air; v_a = 331 m/s
Velocity of sound in water; v_w = 1410 m/s
We are told that frequency is constant and since we want to find the magnitude of the change that occurs in A, then;
I_air = I_water
Thus;
2π² × 331 × 1300 × υ² × Α_a² = 2π² × 1410 × 1000 × υ² × Α_w²
⇒ 331 × 1300 × Α_a² = 1410 × 1000 × Α_w²
⇒ (A_a/A_w)² = (1410 × 1000)/(331 × 1300)
(A_a/A_w)² = 3.2767836393
A_a/A_w = √3.2767836393
A_a/A_w = 1.8
Read more about magnitude of change in amplitude at; https://brainly.com/question/7578880
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